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For $i\\in \\mathbb{F}_q$, let $D_i$ be the subset of $M_2(\\mathbb F_q)$ defined by\n  $ D_i := \\{x\\in M_2(\\mathbb F_q): \\det(x)=i\\}.$ Then our results can be stated as follows. First of all, we show that when $E$ and $F$ are subsets of $D_i$ and $D_j$ for some $i, j\\in \\mathbb{F}_q^*$, respectively, we have $$\\det(E+F)=\\mathbb F_q,$$ whenever $|E||F|\\ge {15}^2q^4$, and then provide a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.07847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-16T17:51:28Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8df515da8b5147aa610c740fb1d4b797b2a51012f17cf502ea2a5d1cc6c6b9ad","abstract_canon_sha256":"3e851fb83f422524d6b3838d4e42f2096697a190aa029ba322074f245fed9038"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:24.058511Z","signature_b64":"E2qjgMKWxsMx16gpQumTcDbo7vx7j+OqJGbjqCt67QJyW/gdAbvXuc9VXqoG7Q4k5l2XUAGwA36zzXk+7LaKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4b718432e21322bfc9b0993920c742874b84fc79baa2c5ca5694210e64f938d","last_reissued_at":"2026-05-17T23:48:24.058126Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:24.058126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution of determinant of sum of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Anh Vinh Le, Daewoong Cheong, Doowon Koh, Thang Pham","submitted_at":"2019-04-16T17:51:28Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be an arbitrary finite field of order $q$. In this article, we study $\\det S$ for certain types of subsets $S$ in the ring $M_2(\\mathbb F_q)$ of $2\\times 2$ matrices with entries in $\\mathbb F_q$. For $i\\in \\mathbb{F}_q$, let $D_i$ be the subset of $M_2(\\mathbb F_q)$ defined by\n  $ D_i := \\{x\\in M_2(\\mathbb F_q): \\det(x)=i\\}.$ Then our results can be stated as follows. First of all, we show that when $E$ and $F$ are subsets of $D_i$ and $D_j$ for some $i, j\\in \\mathbb{F}_q^*$, respectively, we have $$\\det(E+F)=\\mathbb F_q,$$ whenever $|E||F|\\ge {15}^2q^4$, and then provide a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07847","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.07847","created_at":"2026-05-17T23:48:24.058185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07847v1","created_at":"2026-05-17T23:48:24.058185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07847","created_at":"2026-05-17T23:48:24.058185+00:00"},{"alias_kind":"pith_short_12","alias_value":"2S3RQQZOEEZC","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"2S3RQQZOEEZCX7E3","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"2S3RQQZO","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB","json":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB.json","graph_json":"https://pith.science/api/pith-number/2S3RQQZOEEZCX7E3BGJZEDDUFB/graph.json","events_json":"https://pith.science/api/pith-number/2S3RQQZOEEZCX7E3BGJZEDDUFB/events.json","paper":"https://pith.science/paper/2S3RQQZO"},"agent_actions":{"view_html":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB","download_json":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB.json","view_paper":"https://pith.science/paper/2S3RQQZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07847&json=true","fetch_graph":"https://pith.science/api/pith-number/2S3RQQZOEEZCX7E3BGJZEDDUFB/graph.json","fetch_events":"https://pith.science/api/pith-number/2S3RQQZOEEZCX7E3BGJZEDDUFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB/action/storage_attestation","attest_author":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB/action/author_attestation","sign_citation":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB/action/citation_signature","submit_replication":"https://pith.science/pith/2S3RQQZOEEZCX7E3BGJZEDDUFB/action/replication_record"}},"created_at":"2026-05-17T23:48:24.058185+00:00","updated_at":"2026-05-17T23:48:24.058185+00:00"}